61.22.10 problem 10

Internal problem ID [12335]
Book : Handbook of exact solutions for ordinary differential equations. By Polyanin and Zaitsev. Second edition
Section : Chapter 1, section 1.3. Abel Equations of the Second Kind. subsection 1.3.1-2. Solvable equations and their solutions
Problem number : 10
Date solved : Tuesday, January 28, 2025 at 02:47:20 AM
CAS classification : [_rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} y^{\prime } y-y&=-\frac {2 \left (m +1\right )}{\left (m +3\right )^{2}}+A \,x^{m} \end{align*}

✗ Solution by Maple

dsolve(y(x)*diff(y(x),x)-y(x)=-(2*(m+1))/(m+3)^2+A*x^m,y(x), singsol=all)
 

\[ \text {No solution found} \]

✗ Solution by Mathematica

Time used: 0.000 (sec). Leaf size: 0

DSolve[y[x]*D[y[x],x]-y[x]==-(2*(m+1))/(m+3)^2+A*x^m,y[x],x,IncludeSingularSolutions -> True]
 

Not solved